Consider a simple profit maximization problem where there is only one input, labor, denoted by L....

  

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Consider a simple profit maximization problem where there is only one input, labor, denoted by L. Also assume a perfectly competitive market so that the output price, P, is exogenously determined from the market. Let w, denote the exogenous wage rate paid to labor, L. Let F denote the fixed costs of production. Lastly, assume the firm's production function is Q=f(L)=L². a) Substitute the production function into the profit function and write down the profit function to be maximized. b) Use the first order condition to find the solution value for labor, denote it as L* c) Use the second order condition to show that L* is really a maximum. d) Roughly graph the marginal cost (MC) and marginal revenue product of labor (MRPL) curves and show your solution value, L*, on the graph, e) Is the production function, Q = L2, linearly homogeneous? Why or why not? Consider a simple profit maximization problem where there is only one input, labor, denoted by L. Also assume a perfectly competitive market so that the output price, P, is exogenously determined from the market. Let w, denote the exogenous wage rate paid to labor, L. Let F denote the fixed costs of production. Lastly, assume the firm's production function is Q=f(L)=L². a) Substitute the production function into the profit function and write down the profit function to be maximized. b) Use the first order condition to find the solution value for labor, denote it as L* c) Use the second order condition to show that L* is really a maximum. d) Roughly graph the marginal cost (MC) and marginal revenue product of labor (MRPL) curves and show your solution value, L*, on the graph, e) Is the production function, Q = L2, linearly homogeneous? Why or why not?

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